Technically the save file could be easy/automatically shared after each saving. So the implementation is imho more question of fairness and collective playing...
The last part of what you said is the issue...
See, there are quite a few things in this game that only trigger off the host or the host's progress/achievements. Like, you can't get a Statue of Perfection if someone else were to start a game, bring in farmhands (of which you are one) and then never play again while you and the other farmhands keep going.
Also, in the game, one person is the inheritor of the farm. I know, you could be playing it as a commune with friends (my wife and I play this way), but there's still one person that owns the house (the host) and other people that live in cabins. We would have to change a pretty fundamental way that the farm is set up to make it collectively owned instead.
In the meantime... there's always gotta be a primary in some way, and the farmhands playing without that primary? You're advancing days that person needs in order to accomplish goals in order to get things (like the aforementioned statue).